In this paper, the author study the throttling process of the Rotating Bardeen-AdS black hole in a systematic way. In the exended phase space, the mass of black holes should be viewed as entheply. We derive the Joule-Thomson coefficient $μ$ explicitly, and with numerical method, we depict the inversion curves and isenthalpic curves with different parameter $J$ and $g$. It is found that there are only minimum inversion temperature but no maximum inversion temperture, and the ratio between minimum inversion temperature $T_{min}$ and critical temperature $T_C$ is a little greater than $1/2$, and increase with the nonlinear parameter $g$. Furthermore, the shapes of the isenthalpic curves are similar to most case studied before, we calculate the inversion point exists as long as the mass is no less than a certain value $M_{min}$, the effect of the parameter $g$ on the throttling process is also discussed.
The throttling process of the Kerr-Newman-anti-de Sitter (KN-AdS) black holes is systematically studied in the extended phase space. In this framework, the cosmological constant is interpreted as a varying thermodynamic pressure, and the black hole mass is identified with enthalpy. The throttling process is essentially an isenthalpic (i.e., constant-mass) process for the KN-AdS black holes. The Joule-Thomson coefficient, inversion temperature, inversion curve, and isenthalpic curve are investigated in order, with both analytical and numerical methods. It is found that there are no maximum inve…
In this paper, we attempt to study the Joule-Thomson expansion for the regular black hole in an anti-de Sitter background, and obtain the inversion temperature and curve for the Bardeen-AdS black hole in the extended phase space. We investigate the isenthalpic and inversion curves for the Bardeen-AdS black hole in the T-P plane to find the intersection points between them are exactly the inversion points discriminating the heating process from the cooling one. And, the inversion curve for the regular(Bardeen)-AdS black hole is not closed and there is only a lower inversion curve in contrast wi…
The Joule-Thomson expansion process is studied for Bardeen-AdS black holes in the extended phase space. Firstly, we get Joule-Thomson coefficient and find that the divergent point of Joule-Thomson coefficient coincides with the zero point of temperature. The inversion curves are also obtained from the zero point of Joule-Thomson coefficient. Then the minimum inversion temperature and the corresponding mass are obtained. In addition, the ratio between minimum inversion and critical temperature for Bardeen-AdS black holes is also calculated. We obtain the isenthalpic curve in $T$-$P$ graph and d…
We consider the Gauss-Bonnet corrected Bardeen black hole solution in 4-D AdS space-time. The solution is obtained by the limiting procedure adopted by Glavan and Lin in 4-D Einstein-Gauss-Bonnet gravity. The general form of first law of black hole thermodynamics is utilized to calculate various thermodynamics variables. The solution exhibit P-v criticality and belong to the universality class of van-der Waals fluid. The effect of Gauss-Bonnet coupling is investigated on critical parameters and inversion temperature.
We present a $D$-dimensional Bardeen like Anti-de Sitter (AdS) black hole solution in Einstein-Gauss-Bonnet (EGB) gravity, \textit{viz}., Bardeen-EGB-AdS black holes. The Bardeen-EGB-AdS black hole has an additional parameter due to charge ($e$), apart from mass ($M$) and Gauss-Bonnet parameter ($α$). Interestingly, for each value of $α$, there exist a critical $e = e_E$ which corresponds to an extremal regular black hole with degenerate horizons, while for $e< e_E$, it describes non-extremal black hole with two horizons. Despite the complicated solution, the thermodynamical quantities, like t…
We study the motion of a ring string in the background of the Bardeen-AdS black hole surrounded by the quintessence dark energy. The effects of the magnetic monopole charge, the quintessence state parameter, and the quintessence normalization parameter on the dynamical behavior of the ring string are respectively analyzed. Our numerical results show that the chaotic behavior of string generally becomes stronger with the increase of the quintessence normalization parameter. In particular, the conditions for the existence of chaos are distinctly diverse for two different quintessence state param…
We investigate the thermodynamic phase transitions and heat engine efficiency in regular Bardeen AdS black hole. Interpreting cosmological constant as thermodynamic pressure, we study the thermodynamics using T S and P v plots. Specific heat studies also carried out in detail. A first order phase transition in evident from these studies. These are followed by the construction of a heat engine considering the black hole as working substance. The efficiency is obtained via a thermodynamic cycle in the P V plane which receives and ejects heat. The heat engine efficiency is improved by adding a qu…
In the present paper, we investigate the required anisotropy of an exact regular Bardeen black hole characterized by its mass $M$, the nonlinear parameter $g$, the quintessence field parameter $a$ in anti-de sitter spacetime with a static quintessence matter field. We also show that the relative pressure anisotropy, equation of state and the pressure depends on radial coordinate, reflecting the required anisotropy for Bardeen black hole in the quintessence background. Next, we analyze the Joule-Thompson ($JT$) expansion of the black hole spacetime. Treating the cosmological constant as thermod…
Using the Hamilton-Jacobi method, we study certain optical shadows of rotating Bardeen-AdS black holes in the presence of internal and external field contributions. Precisely, we examine the shadow using one-dimensional real curves. By establishing the equations of motion of such AdS black holes without external dark sectors, we first analyze the shadow configurations in terms of a reduced moduli space involving only internal parameter contributions including the charge of the nonlinear electrodynamics. Among others, we find that this parameter serves as a geometric quantity controlling the sh…
Mean first passage time and the Kramers escape rate of phase transitions for the Bardeen-AdS-class black hole
Northwest University（西北大学）；Institute of Modern Physics, Northwest University（西北大学现代物理研究所）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）；Shaanxi Key Laboratory for Theoretical Physics Frontiers（陕西理论物理前沿重点实验室）；Fundamental Discipline Research Center for Quantum Science and technology of Shaanxi Province（陕西省量子科学与技术基础学科研究中心）
We investigate thermodynamics and geometrothermodynamics of regular Bardeen AdS black hole with quintessence. The thermodynamics of the black hole is studied using temperature-entropy ($T-S$) , Pressure-Volume ($P-v$), and Gibbs energy plots, which indicate a critical behaviour.This is also confirmed from the divergence of specific heat against entropy, which shows a second-order phase transition. Moreover, we observe that the quintessence state parameter $ω$ shifts the transition point to lower entropy values. Using the concept of thermodynamic Ruppeiner and Weinhold geometry, we calculated t…
Thermodynamics of Bardeen AdS black holes has attracted a great deal of attentions due to its intrinsic complications and rich phase structures. However, the entropy and thermodynamic volume are incorrect in some literatures. In this paper we revisit the thermodynamics of Bardeen AdS black holes and provide the correct entropy and thermodynamic volume. Furthermore, thermodynamic geometries are a powerful tool to probe the microstructure of black holes. Based on the Hessian matrix of black hole mass, we introduce a thermodynamic metric and give its scalar curvature in Weinhold's geometry. The c…
Thermal chaos under spatially/temporally periodic perturbations in the extended phase space of Bardeen-AdS black holes surrounded by quintessence dark energy is investigated. The occurring condition of chaos is obtained with the Melnikov integral. It is shown that spatial chaos is always supposed to occur even for a tiny spatially periodic perturbation imposed on the equilibrium configuration. However, the temporal chaos will arise in the unstable spinodal region only if the given perturbed amplitude γ is larger than a critical value γc. The value of γc is determined by the magnetic monopole c…
Instead of the work \cite{1} which in according to the Lovelock theorem it could not applicable for all types of 4D curved spacetimes of Einstein Gauss Bonnet (EGB) gravity, authors of the work \cite{2} applied break of diffeomorphism property to present a consistent EGB gravity theory. In this work we use the latter model by adding a nonlinear electromagnetic field lagrangian density to study affects of GB coupling constant into the thermodynamic phase transition and Joule Thomson (JT) adiabatic expansion of a 4D $dS/AdS$ GB Bardeen black hole.
This paper presents an exact solution of Bardeen black hole in presence of massive gravity, which is characterized by the additional parameter $m$. Here, we focus on $4D$ Bardeen AdS massive black hole solutions as example to discuss the thermodynamical properties such as temperature, entropy and specific heat at constant pressure. We also study the critical behaviour of Bardeen AdS massive black holes by considering the cosmological constant $Λ$ as thermodynamical variable (pressure) as well as the parameter associated with the nonlinear electrodynamics. We calculate the critical value of pre…
We study the phase structure and the microscopic interactions in regular Bardeen AdS black hole. The stable and metastable phases in the black hole are analysed through coexistence and spinodal curves. The solutions are obtained numerically as the analytic solution to the coexistence curve is not feasible. The $P_r-T_r$ coexistence equation is obtained using a fitting formula. The coexistence and spinodal curves are plotted in $P_r-T_r$ and $T_r-V_r$ planes to explore the phase structure of the black hole. In the second part of our study, we were able to probe the microscopic interactions of r…
The dependence of the black hole (BH) shadow and thermodynamics may be structured in the regular spacetime. Taking the regular Bardeen-AdS BH as an example, the relationship between the shadow radius and the event horizon radius is derived. It is found that these two radii display a positive correlation, implying that the BH temperature can be rewritten as a function of shadow radius in the regular spacetime. By analyzing the phase transition curves under the shadow context, we found that the shadow radius can replace the event horizon radius to present the BH phase transition process, and the…
In this letter we investigate the throttling process of the charged Anti-de Sitter (AdS) black holes in the rainbow gravity. In the extended phase space of these black holes, the cosmological constant plays the role of a varying thermodynamic pressure and the black hole mass is identified with the thermodynamic enthalpy. We derive exact expressions for the Joule-Thomson coefficient and the inversion temperature in terms of black hole parameters and constants of rainbow gravity analytically, and then perform a numerical analysis for the isenthalpic and inversion curves of charged AdS black hole…
The regular (Bardeen)-AdS (BAdS) black hole (BH) in the extended phase space is taken as an example for investigating the BH phase transition grade from both macroscopic and microscopic points of view. The equation of state and thermodynamic quantities of this BH are obtained. It is found that the BAdS BH phase space in the extended phase space should be a second-order phase transition near the critical point by verifying the Ehrenfest's equation, and the possibility of its first-order phase transition can be ruled out by the entropy continuity and the heat capacity mutation. The critical expo…
In the extended phase space, a general method is used to derive all the possible adiabatic processes for charged AdS black hole. Two kinds are found, one is zero temperature adiabatic process which is irreversible, the other is isochore adiabatic process which is reversible. For the zero temperature adiabatic expansion process, entropy is increasing; pressure, enthalpy, Gibbs free energy and internal energy are decreasing; system's potential energy is transformed to the work done by the system to the outer system. For the isochore adiabatic process, entropy and internal energy are fixed; tempe…
Employing the free energy landscape, we study the phase transition and its dynamics for a class of regular black holes in Anti-de Sitter spacetime governed by the coupling of non-linear electrodynamics, which reduces to Hayward and Bardeen solutions for particular values of spacetime parameters. The Fokker-Planck equation is solved numerically by imposing the reflecting boundary condition and a suitable initial condition, using which, we investigate the probabilistic evolution of regular AdS black holes. In this approach, the on-shell Gibbs free energy is treated as a function of the radius of…
Our primary goal in this paper is to confirm new universal relations in black hole thermodynamics. We investigate the universal relations by selecting different black holes. First, we obtain the black holes' thermodynamic relations assuming a new minor correction is added to the AdS part of the action. Then we confirm the universal relations by performing a series of direct calculations. It is noteworthy that according to each of the properties related to black holes, a new universal relation can be obtained according to this method. We confirm two different types of these universal relations …
In this paper, we attempt to further study the heat engine efficiency for the regular black hole (BH) with an anti-de Sitter (AdS) background where the working material is the Hayward-AdS (HAdS) BH. In the extended phase space, we investigate the heat engine efficiency of the HAdS BH by defining the cosmological constant as the thermodynamic pressure $P$ and deriving the mechanical work from the $PdV$ terms. Then, we obtain the relation between the efficiency and the entropy/pressure and plot these function figures. Meanwhile, we compare the relation between the HAdS BH with that of the Bardee…
Extended thermodynamics and $P-v$ Criticality of Kalb-Ramond black hole coupled with nonlinear electrodynamics
Inter-University Center of Astronomy and Astrophysics (IUCAA)（大学间天文学与天体物理中心）；Department of Physics, Institute of Applied Science and Humanities, GLA University（GLA大学应用科学与人文学院物理系）；School of Physics, Damghan University（达姆甘大学物理学院）；Department of Physics, K.L.S. College, Magadh University（马加德大学K.L.S.学院物理系）；Indian Institute of Engineering Science and Technology (IIEST)（印度工程科学与技术研究所）；Department of General & Theoretical Physics, L. N. Gumilyov Eurasian National University（L.N. 古米廖夫欧亚国立大学普通与理论物理系）
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (``Love'') SL$(2,\mathbb{R})$ symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL$(2,\mathbb{R})$ representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL$\left(2,\mathbb{R}\right)$ representations. It is this highest weight property that forces the static Love numbers to vanish. We f…
